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Appl. Sci. 2016, 6(5), 149; doi:10.3390/app6050149

Mathematical Modeling of Bacteria Communication in Continuous Cultures

1
Faculty for Mathematics and Informatics, Universität Heidelberg, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany
2
Faculty for Mathematics, Technische Universität München, Boltzmannstraße 3, D-85748 Garching bei München, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Yang Kuang
Received: 30 March 2016 / Revised: 2 May 2016 / Accepted: 3 May 2016 / Published: 16 May 2016
(This article belongs to the Special Issue Dynamical Models of Biology and Medicine)
View Full-Text   |   Download PDF [613 KB, uploaded 17 May 2016]   |  

Abstract

Quorum sensing is a bacterial cell-to-cell communication mechanism and is based on gene regulatory networks, which control and regulate the production of signaling molecules in the environment. In the past years, mathematical modeling of quorum sensing has provided an understanding of key components of such networks, including several feedback loops involved. This paper presents a simple system of delay differential equations (DDEs) for quorum sensing of Pseudomonas putida with one positive feedback plus one (delayed) negative feedback mechanism. Results are shown concerning fundamental properties of solutions, such as existence, uniqueness, and non-negativity; the last feature is crucial for mathematical models in biology and is often violated when working with DDEs. The qualitative behavior of solutions is investigated, especially the stationary states and their stability. It is shown that for a certain choice of parameter values, the system presents stability switches with respect to the delay. On the other hand, when the delay is set to zero, a Hopf bifurcation might occur with respect to one of the negative feedback parameters. Model parameters are fitted to experimental data, indicating that the delay system is sufficient to explain and predict the biological observations. View Full-Text
Keywords: quorum sensing; chemostat; mathematical model; differential equations; delay; bifurcations; dynamical system; numerical simulation quorum sensing; chemostat; mathematical model; differential equations; delay; bifurcations; dynamical system; numerical simulation
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Barbarossa, M.V.; Kuttler, C. Mathematical Modeling of Bacteria Communication in Continuous Cultures. Appl. Sci. 2016, 6, 149.

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